On the long-wave approximation for the Euler-Poisson system

We study the long wave approximation to the Euler-Poisson system for the ion-acoustic wave in cold plasma according to the spatial-temporal scale and the amplitude of waves. We first justify rigorously that in the long-wave limit, the one-way propagating solutions of the Euler-Poisson system are well approximated by the unidirectional solutions of the Burger-sor KdV equation with responding to the different parameter scales. We then demonstrate that the solutions could be convergent to two wave packets in opposite directions, where each wave packet involves independently as a solution of the Burgers-or KdV equation. (C) 2020 Elsevier Inc. All rights reserved.